A strategy for time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function

1985 ◽  
Vol 83 (6) ◽  
pp. 3009-3027 ◽  
Author(s):  
Shin‐Ichi Sawada ◽  
Robert Heather ◽  
Bret Jackson ◽  
Horia Metiu
1992 ◽  
Vol 96 (3) ◽  
pp. 2077-2084 ◽  
Author(s):  
Thanh N. Truong ◽  
John J. Tanner ◽  
Piotr Bala ◽  
J. Andrew McCammon ◽  
Donald J. Kouri ◽  
...  

Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.


2018 ◽  
Vol 73 (9) ◽  
pp. 1269-1278
Author(s):  
Min-Ho Lee ◽  
Chang Woo Byun ◽  
Nark Nyul Choi ◽  
Dae-Soung Kim

2018 ◽  
Vol 207 ◽  
pp. 199-216 ◽  
Author(s):  
Lara Martinez-Fernandez ◽  
Roberto Improta

The energetics of the two main proton coupled electron transfer processes that could occur in DNA are determined by means of time dependent-DFT calculations, using the M052X functional and the polarizable continuum model to include solvent effect.


2015 ◽  
Vol 93 (8) ◽  
pp. 841-845 ◽  
Author(s):  
I.A. Pedrosa ◽  
Alberes Lopes de Lima ◽  
Alexandre M. de M. Carvalho

We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola–Kanai oscillator.


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